Surface Area of Right Rectangular Prism
2026-02-28 08:51 Diff
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Last updated on September 4, 2025

A right rectangular prism is a 3-dimensional shape with six rectangular faces, where all angles are right angles. The surface area of a right rectangular prism is the total area covered by its outer surface. It includes the areas of all six faces. In this article, we will learn about the surface area of a right rectangular prism.

What is the Surface Area of a Right Rectangular Prism?

The surface area of a right rectangular prism is the total area occupied by the faces of the prism. It is measured in square units.

A right rectangular prism, also known as a cuboid, has two rectangular bases and four lateral rectangular faces. Its six faces are composed of three pairs of opposite rectangles.

The surface area is calculated by finding the area of each face and summing them all together.

Surface Area of a Right Rectangular Prism Formula

A right rectangular prism consists of six rectangular faces: two length by width, two width by height, and two height by length.

The total surface area is the sum of the areas of these faces. The formula for the total surface area (TSA) of a right rectangular prism is: Total Surface Area = 2lw + 2lh + 2wh 

Where l  is the length,  w  is the width, and  h  is the height of the prism.

Understanding the Surface Area Formula

The total surface area of a right rectangular prism accounts for all the faces of the prism. Each pair of opposite faces has the same area, which simplifies the calculation.

The formula is derived by adding up the areas of these pairs: TSA = 2(lw + lh + wh)  This formula ensures that all six faces are included in the calculation.

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Example Problem: Surface Area Calculation

To calculate the surface area of a right rectangular prism, measure the length, width, and height, then substitute these values into the formula.

For instance, if a prism has a length of 4 cm, a width of 3 cm, and a height of 5 cm, its surface area would be:  TSA = 2(4 x 3 + 3 x 5 + 5 x 4) = 2(12 + 15 + 20) = 2(47) = 94 cm2 

Volume of a Right Rectangular Prism

The volume of a right rectangular prism shows how much space is inside it. It is calculated by multiplying the length, width, and height of the prism:

Volume = l x w x h  This formula tells us the capacity of the prism or how much it can hold.

Ignoring the Pairing of Opposite Faces

Students may forget that opposite faces are equal in area. This can lead to errors in calculating the total surface area. Always remember that each pair of opposite faces contributes twice their area.

Problem 1

Given l = 8 cm, w = 5 cm, h = 7 cm. Use the formula: \(\text{TSA} = 2(lw + lh + wh) = 2(8 \times 5 + 5 \times 7 + 7 \times 8) = 2(40 + 35 + 56) = 2(131) = 262 \text{ cm}^2\)

Okay, lets begin

Find the total surface area of a right rectangular prism with length 10 cm, width 4 cm, and height 6 cm.

Explanation

Surface Area = 248 cm²

Well explained 👍

Problem 2

Use the formula: \(\text{TSA} = 2(lw + lh + wh) = 2(10 \times 4 + 4 \times 6 + 6 \times 10) = 2(40 + 24 + 60) = 2(124) = 248 \text{ cm}^2\)

Okay, lets begin

A right rectangular prism has a length of 12 cm, a width of 7 cm, and a height of 9 cm. Find the surface area.

Explanation

Surface Area = 678 cm²

Well explained 👍

Problem 3

Use the formula: \(\text{TSA} = 2(lw + lh + wh) = 2(12 \times 7 + 7 \times 9 + 9 \times 12) = 2(84 + 63 + 108) = 2(255) = 678 \text{ cm}^2\)

Okay, lets begin

Calculate the surface area of a right rectangular prism with dimensions 3 cm, 4 cm, and 5 cm.

Explanation

Surface Area = 94 cm²

Well explained 👍

Problem 4

Use the formula: \(\text{TSA} = 2(lw + lh + wh) = 2(3 \times 4 + 4 \times 5 + 5 \times 3) = 2(12 + 20 + 15) = 2(47) = 94 \text{ cm}^2\)

Okay, lets begin

The surface area of a right rectangular prism is 214 cm². If its length is 7 cm and width is 5 cm, find its height.

Explanation

Height = 6 cm

Well explained 👍

It is the total area that covers the outside of the prism, including all its rectangular faces.

1.What is the formula for surface area of a right rectangular prism?

The formula is TSA = 2lw + 2lh + 2wh  where  l ,  w , and h  are the length, width, and height.

2.How do you differentiate surface area from volume?

Surface area is the total area of all outer faces of a shape, while volume measures the space inside the shape.

3.Are the opposite faces of a right rectangular prism equal?

Yes, each set of opposite faces in a right rectangular prism has the same area.

4.What unit is surface area measured in?

Surface area is always measured in square units like cm², m², or in².

Common Mistakes and How to Avoid Them in the Surface Area of a Right Rectangular Prism

Students often make mistakes while calculating the surface area of a right rectangular prism, leading to incorrect answers. Below are some common mistakes and ways to avoid them.

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Seyed Ali Fathima S

About the Author

Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.

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